If 5 sec θ - 3 tan θ = 5, then what is the value of 5 tan θ - 3 sec θ?

Given : $$5sec\theta-3tan\theta=5$$

Squaring both sides, we get :

=> $$(5sec\theta-3tan\theta)^2=(5)^2$$

=> $$25sec^2\theta+9tan^2\theta-2(5sec\theta)(3tan\theta)=25$$

Using, $$sec^2\theta-tan^2\theta=1$$

=> $$25(1+tan^2\theta)+9(sec^2\theta-1)-30(tan\theta)(sec\theta)=25$$

=> $$25+25tan^2\theta+9sec^2\theta-9-2(5tan\theta)(3sec\theta)=25$$

=> $$(5tan\theta)^2+(3sec\theta)^2-2(5tan\theta)(3sec\theta)=9$$

=> $$(5tan\theta-3sec\theta)^2=(3)^2$$

=> $$5tan\theta-3sec\theta=3$$

=> Ans - (C)